Fundamentals
The core facts every aspirant should own — each a titled nugget with a real-world story, the concept in plain words, and a memory trick. Works even when the internet doesn't.
1,200 fundamentals
“Neon signs glow because electrons jump between these fixed rungs, emitting exact colours.”
Electrons occupy fixed energy levels; for hydrogen Eₙ = −13.6/n² eV.
Eₙ = −13.6/n² eV
Memory trick: Bound electron → negative energy.
A changing electric field produces magnetic effects and a changing magnetic field produces an electric field. This coupled disturbance can travel through vacuum without charges continuously carrying it forward.
Memory trick: changing E makes B; changing B makes E.
Gravity changes only the vertical velocity of a projectile. Horizontally, velocity stays constant when air resistance is ignored. The two motions share the same clock but otherwise evolve independently.
Memory trick: one clock, two equations: solve x and y separately, then recombine.
A frequent error is treating a hole in a heated metal plate as shrinking. In reality, Most materials expand when heated because the average separation between particles increases. For an isotropic solid, area and volume expansion coefficients are approximately 2alpha and 3alpha when alpha is small.
Memory trick: heat the whole drawing: the hole expands as if it were made of the same material.
For an ideal gas, absolute temperature measures average translational kinetic energy per molecule: 3k_BT/2. At the same temperature, light and heavy molecules have the same average translational energy but different rms speeds.
Memory trick: same average energy, lighter molecules move faster.
The electric field points in the direction in which potential decreases most rapidly. Along one dimension E_x = -dV/dx; the minus sign carries the direction information.
Memory trick: a positive test charge naturally moves downhill in potential.
Cutting a bar magnet produces smaller north-south dipoles, not separate monopoles. Therefore net magnetic flux through any closed surface is zero.
Memory trick: every cut makes two complete magnets.
Bohr allowed only orbits with angular momentum n h/(2pi). An electron in a stationary orbit does not radiate; light is emitted or absorbed only during a transition.
Memory trick: no light within an orbit; photon only during a jump.
A bound nucleus has less mass than its separated nucleons. The missing mass corresponds to the energy released during binding: B = Delta m c^2.
Memory trick: separated nucleons minus nucleus gives positive mass defect.
Accuracy means closeness to the accepted value; precision means repeatability. Repeated measurements can reduce random uncertainty but cannot remove a systematic calibration error.
Memory trick: tight cluster is precise; correct centre is accurate.
When waves overlap, their displacements add algebraically at each point. Constructive and destructive interference are consequences of this linear addition, not permanent destruction of energy.
Memory trick: add displacements with phase first, then find intensity.
A velocity component perpendicular to B produces circular motion, while a parallel component remains unchanged. Together they make a helix whose pitch depends on the parallel speed.
Memory trick: v_perp sets radius; v_parallel sets pitch.
Bright fringes form where the path difference is a whole number of wavelengths, dark where it's an odd number of half-wavelengths.
Memory trick: path diff = nλ → bright; (n+½)λ → dark.
The effective (root-mean-square) value of AC that delivers the same heating as a steady DC; Vrms = V0/√2.
Memory trick: 220 V mains is the rms value; the peak is about 311 V.
The charge-free zone at a p–n junction that sets up a built-in barrier potential.
Memory trick: it's 'depleted' of carriers — that's what creates the barrier.
“Hold a finger up and blink each eye: it jumps. Astronomers use Earth's orbit as their 'two eyes'.”
Very large distances (like to nearby stars) are found by parallax — the apparent shift of an object against a far background when viewed from two points.
Memory trick: Bigger baseline → measure farther.
“The ½at² term is why a dropped ball falls farther in each successive second.”
Displacement under constant acceleration is s = ut + ½at².
s = ut + ½at²
Memory trick: distance = start×time + half×accel×time².
“A slow-moving truck can carry more momentum than a fast bullet.”
Momentum p = mv is 'mass in motion'; a net force is needed to change it.
p = mv
Memory trick: p = mv.
“Water held behind a dam is stored energy waiting to become electricity.”
Stored energy of position: gravitational PE = mgh near Earth.
PE = mgh
Memory trick: Height stores energy.
“A solid cylinder beats a hollow one down a ramp — less energy 'wasted' spinning.”
A rolling body has both translational (½mv²) and rotational (½Iω²) kinetic energy.
KE = ½mv² + ½Iω²
Memory trick: Rolling = moving + spinning energy.
“The ISS orbits at ~7.8 km/s — forever 'falling' around Earth.”
Speed needed to stay in a circular orbit, v = √(GM/r).
v = √(GM/r)
Memory trick: Faster orbit = lower altitude.
“Aeroplane wings lift because air rushes faster over the top, lowering the pressure there.”
In a flowing fluid, faster flow means lower pressure.
P + ½ρv² + ρgh = const
Memory trick: Fast flow = low pressure.
A frequent error is giving strain the unit metre. In reality, Stress measures internal restoring force per area; strain measures fractional deformation. Stress has pressure units, while strain is dimensionless.
Memory trick: stress is cause per area; strain is fractional response.
“Flick a rope for transverse; push a slinky for longitudinal.”
In transverse waves particles move perpendicular to travel (light, strings); in longitudinal waves they move along it (sound).
Memory trick: Sound = longitudinal; light = transverse.